What’s in a Name? Medellin and the Many Meanings of "Binding"

Is
Medellin
really a case about the role of courts in enforcing international law or is it instead a case about whether international law is binding and who can make it so?
And is there a difference between these two possibilities?

On first glance, all Roberts is saying is that the President can’t force state courts to abide by a an ICJ opinion regarding the Vienna Conventions when doing so would conflict with a state’s own state court procedures. He quite reasonably – it seems to me – concludes that Congress never authorized the president to exercise such power over states courts and in fact is probably best read to have impliedly prohibited him from doing so.
But there’s a lot of loose language suggesting the President can never make non-self executing treaties "binding," which suggests that the president couldn’t even bind federal officers to adhere to their terms.
Insofar as Roberts’s opinion rests on an implicit construction of congressional intent in this partiuclar case – and a judgment that Congress would not have wanted the president to exercise this power over state courts, it need not be read to go very far.
And even insofar as it holds that the ICJ decision does not itself give rise to a privately enforceable right, it’s not all that surprising a ruling. But the loose language regarding bindingness may not be accidental.
So,
Medellin
may not really be about the role of courts in enforcing international law at all; it may be instead about the extent which non-self executing provisions of international law – from the Torture Convention on down -- can’t be made binding in any respect on any federal officers. If that’s the real import of Roberts’s opinion, it’s big one and goes well beyond the issue of the role that courts can play in giving effect to international law.